Make things as simple as possible, but not simpler ! Albert Einstein Albert Einstein‘s razor, precise refence is unknown.
The paradigm of structural biology
The paradigm of structural biology
The paradigm of structural biology
The paradigm of structural biology
The paradigm of structural biology
James D. Watson, 1928-, and Francis H.C. Crick, 1916-2004 Nobel prize 1962 1953 – 2003 fifty years double helix The three-dimensional structure of a short double helical stack of B-DNA
N = 4 n N S < 3 n Criterion: Minimum free energy (mfe) Rules: _ ( _ ) _ { AU , CG , GC , GU , UA , UG } A symbolic notation of RNA secondary structure that is equivalent to the conventional graphs
Taq = thermus aquaticus The logics of DNA replication
1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives
Nucleobase and base pair mutations
Nucleobase and base pair mutations
Nucleobase and base pair mutations
A case study: A simple RNA molecule
1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives
The inverse folding algorithm searches for sequences that form a given RNA secondary structure under the minimum free energy criterion.
Inversion of genotype-phenotype mapping
Neutral networks in sequence space
Realistic fitness landscapes 1.Ruggedness: nearby lying genotypes may unfold into very different phenotypes 2.Neutrality: many different genotypes give rise to phenotypes with identical selection behavior
1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives
Three necessary conditions for Darwinian evolution are: 1. Multiplication, 2. Variation , and 3. Selection. Charles Darwin, 1809-1882 All three conditions are fulfilled not only by cellular organisms but also by nucleic acid molecules – DNA or RNA – in suitable cell-free experimental assays: Darwinian evolution in the test tube
Evolution in the test tube: G.F. Joyce, Angew.Chem.Int.Ed. 46 (2007), 6420-6436
Christof K. Biebricher, 1941-2009 Kinetics of RNA replication C.K. Biebricher, M. Eigen, W.C. Gardiner, Jr. Biochemistry 22 :2544-2559, 1983
RNA replication by Q -replicase C. Weissmann, The making of a phage . FEBS Letters 40 (1974), S10-S18
stable does not replicate! metastable replicates! C.K. Biebricher, R. Luce. 1992. In vitro recombination and terminal recombination of RNA by Q replicase. The EMBO Journal 11:5129-5135.
x d n j W x x Φ j n ; 1 , 2 , , ji i j i dt 1 n n Φ f x x i i i i i 1 1 Manfred Eigen 1927 - Mutation and (correct) replication as parallel chemical reactions M. Eigen. 1971. Naturwissenschaften 58:465, M. Eigen & P. Schuster.1977. Naturwissenschaften 64:541, 65:7 und 65:341
Mutation-selection equation : [I i ] = x i 0, f i > 0, Q ij 0 dx n n n i f Q x x i n x f x f , 1 , 2 , , ; 1 ; j ji j i i j j dt j i j 1 1 1 Solutions are obtained after integrating factor transformation by means of an eigenvalue problem n 1 c t 0 exp n ik k k x t k i n c h x 0 ; 1 , 2 , , ; ( 0 ) ( 0 ) i k ki i n n 1 i 1 c t 0 exp jk k k j k 1 0 1 W f Q i j n L i j n L H h i j n ; , 1 , 2 , , ; ; , 1 , 2 , , ; ; , 1 , 2 , , i ij ij ij 1 L W L k n ; 0 , 1 , , 1 k
quasispecies driving virus populations through threshold The error threshold in replication and mutation
single peak landscape step linear landscape Model fitness landscapes I
Error threshold on the single peak landscape
Error threshold on the step linear landscape
linear and multiplicative hyperbolic Model fitness landscapes II
The linear fitness landscape shows no error threshold
single peak landscape „realistic“ landscape Rugged fitness landscapes over individual binary sequences with n = 10
Error threshold: Individual sequences n = 10, = 2, s = 491 and d = 0, 0.5, 0.9375
d = 0.5 d = 1.0 Case I : Strong quasispecies n = 10, f 0 = 1.1, f n = 1.0, s = 919
d = 0.995 d = 1.0 Case III : multiple transitions n = 10, f 0 = 1.1, f n = 1.0, s = 637
1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives
Motoo Kimuras population genetics of neutral evolution. Evolutionary rate at the molecular level. Nature 217 : 624-626, 1955. The Neutral Theory of Molecular Evolution . Cambridge University Press. Cambridge, UK, 1983.
Motoo Kimura Is the Kimura scenario correct for frequent mutations?
d H = 1 x p x p lim ( ) ( ) 0 . 5 p 0 1 2 d H = 2 x p a lim ( ) p 0 1 x p a lim ( ) 1 p 0 2 d H 3 x p x p lim ( ) 1 , lim ( ) 0 or p p 0 1 0 2 x p x p lim ( ) 0 , lim ( ) 1 p p 0 1 0 2 Random fixation in the Pairs of neutral sequences in replication networks sense of Motoo Kimura P. Schuster, J. Swetina. 1988. Bull. Math. Biol. 50:635-650
A fitness landscape including neutrality
Neutral network: Individual sequences n = 10, = 1.1, d = 0.5
Neutral network: Individual sequences n = 10, = 1.1, d = 0.5
Consensus sequence of a quasispecies with strongly coupled sequences of Hamming distance d H (X i, ,X j ) = 1 and 2.
0 , 0 largest eigenvalue and eigenvector diagonalization of matrix W „ complicated but not complex “ W = G F mutation matrix fitness landscape „ complex “ ( complex ) sequence structure „ complex “ mutation selection Complexity in molecular evolution
1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives
Evolution in silico W. Fontana, P. Schuster, Science 280 (1998), 1451-1455
Replication rate constant : f k = / [ + d S (k) ] d S (k) = d H (S k ,S ) Selection constraint : Population size, N = # RNA molecules, is controlled by the flow N t N N ( ) Mutation rate : p = 0.001 / site replication The flowreactor as a device for studies of evolution in vitro and in silico
In silico optimization in the flow reactor: Evolutionary Trajectory
Randomly chosen initial structure RNA phe as target structure
Randomly chosen initial structure RNA phe as target structure
Randomly chosen initial structure RNA phe as target structure
Randomly chosen initial structure RNA phe as target structure
Evolutionary trajectory Spreading of the population on neutral networks Drift of the population center in sequence space
Richard Lenski, 1956 - Bacterial evolution under controlled conditions: A twenty years experiment. Richard Lenski, University of Michigan, East Lansing
1 year Epochal evolution of bacteria in serial transfer experiments under constant conditions S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants . Science 272 (1996), 1802-1804
1 year Epochal evolution of bacteria in serial transfer experiments under constant conditions S. F. Elena, V. S. Cooper, R. E. Lenski. Punctuated evolution caused by selection of rare beneficial mutants . Science 272 (1996), 1802-1804
The twelve populations of Richard Lenski‘s long time evolution experiment Enhanced turbidity in population A-3
Innovation by mutation in long time evolution of Escherichia coli in constant environment Z.D. Blount, C.Z. Borland, R.E. Lenski. 2008. Proc.Natl.Acad.Sci.USA 105:7899-7906
Contingency of E. coli evolution experiments
1. Adaptation in biology 2. Cycles of evolution 3. Molecules – from sequence to function 4. Mutation and structure 5. Spaces and mappings 6. Evolutionary dynamics on landscapes 7. Neutrality 8. Stochasticity, contingency, and history 9. Perspectives
(i) Fitness landscapes for the evolution of molecules are obtainable by standard techniques of physics and chemistry. (ii) Fitness landscapes for evolution of viroids and viruses under controlled conditions are accessible in principle. (iii) Systems biology can be carried out for especially small bacteria and an extension to bacteria of normal size is to be expected for the near future. (iv) The computational approach for selection on known fitness landscapes – ODEs or stochastic processes – is standard. (v) The efficient description of migration and splitting of populations in sequence space requires new mathematical techniques.
Consideration of multistep and nonlinear replication mechanisms as well as accounting for epigenetic phenomena is readily possible within the molecular approach.
Coworkers Walter Fontana , Harvard Medical School, MA Matin Nowak , Harvard University, MA Ivo L.Hofacker , Christoph Flamm , Andreas Svr č ek-Seiler , Universität Wien, AT Universität Wien Peter Stadler , Bärbel Stadler , Universität Leipzig, GE Sebastian Bonhoeffer , ETH Zürich, CH Christian Reidys , University of Southern Denmark, Odense, DK Christian Forst , University of Texas Southwestern Medical Center, TX Kurt Grünberger , Michael Kospach , Andreas Wernitznig , Stefanie Widder, Stefan Wuchty, Universität Wien, AT Jan Cupal , Ulrike Langhammer , Ulrike Mückstein, Jörg Swetina, Universität Wien, AT Ulrike Göbel , Walter Grüner , Stefan Kopp , Jaqueline Weber, Institut für Molekulare Biotechnologie, Jena, GE
Acknowledgement of support Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No. 09942, 10578, 11065, 13093 13887, and 14898 Universität Wien Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No. 98-0189, 12835 (NEST) Austrian Genome Research Program – GEN-AU Siemens AG, Austria Universität Wien and the Santa Fe Institute
Thank you for your attention !
Web-Page for further information: http://www.tbi.univie.ac.at/~pks
Recommend
More recommend
